Question

What is the magnetic force per unit length experienced by wire C as shown in figure ? (Assume that all wires are parallel and indefinitely long)

Answer 1

The force on wire C due to B and A is
$F=F_B+F_c=\frac{{\mu }_0}{4\pi }\frac{2\left(I\right)\left(I\right)}{2d}+\frac{{\mu }_0}{4\pi }\frac{2\left(I\right)\left(I\right)}{(2d+d)}=\frac{{\mu }_{0}2I^2}{4\pi d}(\frac{1}{2}+\frac{1}{3})=\frac{{\mu }_{0}2I^2}{4\pi d}\times \left(\frac{5}{6}\right)=\frac{{5\mu }_0{I}^2}{12\pi d}$.